Universal Anisotropy Index Research Articles

A Reinvestigation of a Superhard Tetragonal sp³ Carbon Allotrope.

–carbon was first proposed by Zhang et al., this paper will report regarding this phase of carbon. The present paper reports the structural and elastic properties of the three-dimensional carbon allotrope –carbon using first-principles density functional theory. The related enthalpy, elastic constants, and phonon spectra confirm that the newly-predicted –carbon is thermodynamically, mechanically, and dynamically stable. The calculated mechanical properties indicate that –carbon has a larger bulk modulus (393 GPa), shear modulus (421 GPa), Young’s modulus (931 GPa), and hardness (55.5 GPa), all of which are all slightly larger than those of c-BN. The present results indicate that –carbon is a superhard material and an indirect-band-gap semiconductor. Moreover, –carbon shows a smaller elastic anisotropy in its linear bulk modulus, shear anisotropic factors, universal anisotropic index, and Young’s modulus.

Ternary addition and site substitution effect on B2 RuHf-based intermetallics: A first-principles study

By using the first-principle supercell calculations, we studied the site substitution and ternary alloying elements M (M=Al, Si, Cu, Zn, Sn, Zr, Ta, Nb, Ti, W, V, Mo, Cr, Os, Rh, Ir, Pd and Pt) effect on the structural, mechanical, thermal and electronic properties of B2 RuHf-based intermetallics. The formation enthalpy H and ternary transfer energy EMHf→Ruof RuHf–M intemetallics are calculated to predict the site preference of M. The elastic parameters including bulk modulus B, shear modulus G, Young' modulus E, B/G ratio, Poisson's ratio υ, universal anisotropic index Au, shear anisotropic factors A1, A2, A3 and directional Young's modulus have been calculated. The results reveal that RuHf and RuHf–M intermetallics without superhard characters are not low-compressive materials. In addition, the anisotropic elastic properties of these compounds are predicted. Also, the results demonstrate the anisotropic acoustic velocities, anisotropic thermal conductivity and potential thermal-insulating application of these compounds. Furthermore, the electronic densities of states (DOS) are calculated to illustrate the electron structures of these compounds and further investigate their structural and mechanical properties.

Elasticity, hardness and anisotropies of bc-B<sub><italic>n</italic></sub>CN (<italic>n</italic>=1, 2, 4)

Based on the first-principles density functional theory with plane wave ultrasoft and norm-conserving pseudo- potential methods, the elasticity and hardness of the three selected bc-B n CN ( n =1, 2, 4) are investigated in details using LDA and GGA potential field. In addition, we pay close attention to their otherness of elastic and plastic anisotropies. The calculated results prove that these three kinds of structures are all stable in thermodynamics. Among these three structures, bc-BCN, which has the maximum absolute values of formation enthalpy and cohesive energy, is the most stable one with the lowest rate of atom B. And the reason why bc-BCN is the most resisting structure and has the largest absolute value of energy is that it owns large number of relatively low energy bonds such as B—N, B—C, C—N bonds and the fewest of B—B bond. The analysis of elasticity and hardness results shows that the values of elastic modulus and hardness decrease accordingly with the increasing ratio of atom B in the system. Then in line with the universal elastic anisotropic index A U, percent elastic anisotropy A B and A G, and shear anisotropic factors A 1, A 2 and A 3 of bc-B n CN ( n =1, 2, 4), it is revealed that all of the three structures show different extent of anisotropy. Among these, bc-BCN displays better anisotropic property than c-BN as a whole. Finally, the ideal stress-strain curves of bc-B n CN ( n =1, 2, 4) are fitted through the simulation of stepped tensile and shear deformation, and it indicates the anisotropy during deformation process. What’s more, the matched curves reveal their respective yield surfaces, which are the easiest to slide. Additionally, the most effortless slip directions of different structures are deduced explicitly. In general, bc-BCN is the most easily to synthesize and most suitable for applications among these three compounds.

Si96: A New Silicon Allotrope with Interesting Physical Properties.

The structural mechanical properties and electronic properties of a new silicon allotrope Si96 are investigated at ambient pressure by using a first-principles calculation method with the ultrasoft pseudopotential scheme in the framework of generalized gradient approximation. The elastic constants and phonon calculations reveal that Si96 is mechanically and dynamically stable at ambient pressure. The conduction band minimum and valence band maximum of Si96 are at the R and G point, which indicates that Si96 is an indirect band gap semiconductor. The anisotropic calculations show that Si96 exhibits a smaller anisotropy than diamond Si in terms of Young’s modulus, the percentage of elastic anisotropy for bulk modulus and shear modulus, and the universal anisotropic index AU. Interestingly, most silicon allotropes exhibit brittle behavior, in contrast to the previously proposed ductile behavior. The void framework, low density, and nanotube structure make Si96 quite attractive for applications such as hydrogen storage and electronic devices that work at extreme conditions, and there are potential applications in Li-battery anode materials.

Elasticity and Anisotropy of Titanium Oxide TixOy

The elastic properties and their anisotropies of Ti x O y (TiO, TiO 2 , Ti 2 O 3 , Ti 3 O, Ti 3 O 5 ) were investigated based on first-principles calculations with the generalized gradient approximation (GGA) . The elastic constants and modulus, Poisson’s ratio and universal anisotropic index were obtained. The bonds properties of the five materials were analyzed through Poisson’s ratio and Pugh modulus ratio (G/B). The five titanium oxides are elastically anisotropic. Details of anisotropies were demonstrated in 3D plots.

First-principles investigation of mechanical and electronic properties of LaAg5 Laves phase under pressure

AbstractThe effects of applied pressure on the structural, mechanical, and electronic properties of LaAg5 compound were investigated employing the first-principles method based on the density functional theory. The mechanical results demonstrated that bulk modulus, shear modulus and Young's modulus presented the linearly increasing dependences on the external pressure; the B/G and Poisson's ratio indicated that LaAg5 compound was a ductile material with central forces in interatomic under pressure from 0 to 40 GPa; the universal anisotropic index was performed to investigate the elastic anisotropic of LaAg5. Additionally, the pressure dependence of the density of states and Mulliken charge were also discussed. The bonding characterization in LaAg5 was composed of metallic, covalent and ionic. The metallic component was derived from free-electron transferring from Ag-s and Ag-d to Ag-p, and from La-s to La-d. The ionic component was due to the charge movement from La to Ag. The covalent was owing to Ag-p-La-d bonding hybridization and Ag-s-Ag-p in the Ag atomic chains. The covalent and ionic bonds were stronger under pressure but there was no significant change in metallic nature.

Physical properties of La2B2O7(B[dbnd]Zr, Sn, Hf and Ge) pyrochlore: First-principles calculations

Using first-principles theory and further verified by the experimental results, we have studied the electronic structure, mechanical and thermal properties of La2B2O7(BZr, Sn, Hf and Ge) pyrochlore. It is shown that the La2B2O7 pyrochlore are charge-transfer-type insulators with the strong ionic bonding. The calculated band gap of La2Zr2O7, La2Sn2O7, La2Hf2O7, and La2Ge2O7 are 4.01, 3.05, 3.13 and 2.42 eV, respectively. The elastic constants, hardness, shear modulus, bulk modulus, Young's modulus and Poisson's ratio of La2B2O7 compounds were investigated systematically. Anisotropic elastic and thermal properties of La2B2O7 compounds were discussed by using Zener's indexes (AZ) and universal elastic anisotropic index (AU). The sound velocities along [100], [110] and [111] directions were calculated for each La2B2O7 compounds. Both Clark's model and Cahill's model were used to evaluate the minimum thermal conductivity of all compounds. According to the Clark's model, when the temperature is much higher than Debye temperature, the minimum thermal conductivity of La2Zr2O7, La2Sn2O7,La2Hf2O7, and La2Ge2O7 are 1.27, 1.24, 1.09 and 1.41 W/m K, respectively. According to the calculated results of these crystals, the La2B2O7 compounds exhibit an extraordinary low thermal conductivity which can be used as thermal insulating materials.

Structural, Elastic, and Electronic Properties of a New Phase of Carbon* *Supported by the National Natural Science Foundation of China under Grant Nos. 61006028 and 61204044

Based on density function theory with the ultrasoft pseudopotential scheme in the frame of the local density approximation and the generalized gradient approximation, the structural, elastic, and electronic properties of carbon with P2221 phase have been systematically studied in this paper. The calculated results show that the P2221 phase of carbon is mechanically stable and dynamically stable at ambient pressure. The anisotropy studies of Young's modulus, Poisson's ratio, shear anisotropic factor, the percentage of elastic anisotropy for bulk modulus, the percentage of elastic anisotropy for shear modulus and the universal anisotropic index show that P2221 phase of carbon exhibits anisotropy. In addition, P2221 phase is an indirect semiconductor with bandgap of 3.423 eV. But, the band gap of P2221 phase for carbon increase with increasing pressure.

Pressure-induced structural transition and thermodynamic properties of NbSi2 from first-principles calculations

Applying the particle swarm optimization algorithm to the crystal structure prediction, we first predict a novel high pressure phase of NbSi2 with Si tetrahedron embedded diamond structure of Nb. NbSi2 alloy undergoes a first-order phase transition from hexagonal phase to cubic phase at about 175 GPa with a volume collapse of 4.1%, indicating the first-order transition. New predicted NbSi2 phase is dynamically stable in the absence of any imaginary phonon frequency in the whole Brillouin zone of phonon spectrum. The calculations of total and partial density of states indicate that the NbSi2 is in hexagonal phase at 0 GPa and it is in cubic structure at 180 GPa, both of which exhibit metal behaviors, which is dominated by Nb atom. There exists obviously the p-d hybridization between Nb and Si, and more charges accumulate in Si tetrahedron. Based on the “stress-strain” method, elastic constants, bulk modulus, shear modulus, Young's modulus, and Debye temperature of NbSi2 in two phases under pressure are systematically investigated using first principles calculations combined with the quasi-harmonic Debye model. To evaluate the ductile and brittle characteristics of NbSi2 alloy, pressure dependence of G/B ratio is investigated. Furthermore, the values of hardness and percent anisotropy AB and AG and the universal anisotropic index AU (inset) for NbSi2 alloy in hexagonal and cubic structures are also calculated. Our results show that external pressure has different effects on the values of ductility and hardness and anisotropy of the two phases. External pressure can improve the ductility of hexagonal phase, while it has a negligible effect on that of cubic phase. The hardness values of two phases of NbSi2 are analyzed in detail by using the G/B ratio. As pressure increases, the elastic anisotropy of hexagonal phase increases rapidly, while that of cubic phase remains unchanged.

Stability and elastic properties of NbxCy compounds

Density functional theory (DFT) is applied to investigate the stability and mechanical properties of NbxCy compounds. The structures of NbxCy compounds are optimized, and the results are in good agreement with previous work. The calculated results of the cohesive energy and the formation enthalpy of NbxCy show that they are thermodynamically stable structures, except for Pmc21-Nb2C. The mechanical properties such as the bulk modulus, Young's modulus, the shear modulus, and Poisson's ratio are obtained by Voigt—Reuss—Hill approximation. The results show that the Young's modulus and shear modulus of NbC are larger than other NbxCy compounds. The mechanical anisotropy is characterized by calculating several different anisotropic indexes and factors, such as universal anisotropic index (AU), shear anisotropic factors (A1, A2, A3), and percent anisotropy (AB and AG). The surface constructions of bulk and Young's moduli are illustrated to indicate the mechanical anisotropy. The hardness of NbxCy compounds is also discussed in this paper. The estimated hardness for all NbxCy compounds is less than 20 GPa.

Theoretical prediction of the fundamental properties for the ternary MgYZn and Mg0.9YZn1.06 alloys

The fundamental properties of the ternary MgYZn and Mg0.9YZn1.06 (Mg–Y–Zn) alloys are investigated by using the first-principles density functional theory within the generalized gradient approximation (GGA). The calculated lattice constants are found in a good agreement with the available experimental data. The calculated elastic constants indicate that both of the Mg–Y–Zn alloys are mechanically stable. The shear modulus, Young’s modulus, Poisson’s ratio σ, the ratio B/G and the universal anisotropy index are also calculated. According to these values, we have revealed that the Mg–Y–Zn alloys behave in a ductile manner and exhibit a strong anisotropy. Finally, the Debye temperature and minimum thermal conductivity are obtained.

First-principles investigation of mechanical, electronic and optical properties of Al3Sc intermetallic compound under pressure

The dependences of the structural, mechanical, electronic and optical properties of Al3Sc intermetallic compound on pressure were studied using the first-principles method based on the density functional theory with generalized gradient approximation and local density approximation methods. The results showed the pressure has the significant impact on the equilibrium volume, mechanical properties, electronic properties and optical properties of Al3Sc. The calculated structural and mechanical parameters (i.e., bulk modulus (B), shear modulus (G), Young’s modulus (E), Poisson’s ratio (v), and Debye temperature (θD)) were in good agreement both with the previously reported experimental and theoretical results at zero pressure. Additionally, all these parameters presented the linearly increasing dependences on the external pressure. The B/G ratios indicated the Al3Sc crystals should exhibit brittle deformation behavior at 0–50GPa. The universal anisotropic index (AU) signified the Al3Sc compound was near elastically isotropic under zero pressure, and may become anisotropic as the pressure increased. Further, the pressure-dependent behaviors of density of states (DOS), Mulliken charge and bond length were discussed. In the DOS spectra, the values of DTotalAl3Sc, DpAl and DdSc were all reduced as the pressure was elevated at the Fermi level. However, the relative contributions to the DTotalAl3Sc from Alp state were found slightly increased, and Sc3d state remained leveled. Finally, the optical conductivity spectra were simulated as a function of the external pressure. The two peak positions in such spectra were successfully identified and compared with other reported values.

First-principles study of mechanical and electronic properties of TiB compound under pressure

The effects of applied pressures on the structural, mechanical and electronic properties of TiB compound were studied using the first-principles method based on the density functional theory. The results showed the pressures have the significant effects on the mechanical properties and electronic properties of TiB phase. The calculated structural and mechanical parameters (i.e., bulk modulus, shear modulus, Young's modulus, Poisson's ratio and Debye temperature) were in good agreement both with the previously reported experimental and theoretical results at zero pressure. Additionally, all these parameters presented the linearly increasing dependences on the external pressure. The B/G ratios signified the TiB crystals should exhibit the brittle deformation behavior at 0–100 GPa. The universal anisotropic index indicated the TiB compound was elastically isotropic under zero pressure, and may become anisotropic at higher pressures. Further, the density of states and Mulliken charge of TiB were discussed. The bonding nature in TiB was a combination of metallic, ionic and covalent at zero pressure. The metallic component was derived from free-electron transfer from the Ti4s to Ti3d and Ti3p states. The ionic component was originated from the charge transfer from Ti to B atoms. The covalent component had two sources. One was from the B2s–B2p hybridization in the B atomic chains. The other one was from B2p–Ti3d bonding hybridization. Under higher pressures, the ionic and covalent bonds were both improved with the rising of pressures. This should be the fundamental reason for the enhanced mechanical properties in the TiB compound. At the same time, the metallic bond kept leveled to ensure the electric conductivity.

FIRST-PRINCIPLES INVESTIGATION OF THE ELECTRONIC, ELASTIC AND THERMODYNAMIC PROPERTIES OF SUPERCONDUCTINGMgB2

The electronic structure, elastic properties, Debye temperature and thermal conductivity of MgB2are investigated by using the first-principles density function theory within the generalized gradient approximation (GGA). The calculated elastic constants indicate that the MgB2is mechanically stable. The shear modulus, Young's modulus, Poisson's ratio, σ, the ratio B/G and universal anisotropy index are also calculated. Finally, the averaged sound velocity, longitudinal sound velocity, transverse sound velocity, Debye temperature and thermal conductivity are obtained.

Stability, elastic properties and electronic structures of L12-ZrAl3 and D022-ZrAl3 up to 40 GPa

The effects of high pressures on structure stability, elastic properties and electronic structures of zirconium trialuminide L12- and D022-ZrAl3 compounds have been investigated by first-principles calculations within the local density approximation. The equilibrium structure and formation energy show that L12-ZrAl3 is more stable than D022-ZrAl3 at the applied pressure. The elastic properties and Debye temperatures of (L12, D022)-ZrAl3 increase with the increasing pressure and the calculated values in the ground state are in good agreement with the available experiment data. The mechanical anisotropic properties were discussed using the universal anisotropic index AU. The sound velocities along the [100], [110] and [111] directions were also calculated for both phases. The calculated electronic properties under high pressures suggest that the decreased electronic density of states (DOS) at the Fermi level and the changed charges distribution lead to the observed decrease of the structural stability for (L12, D022)-ZrAl3 under high pressures.

The Elastic Constants and Anisotropy of Superconducting MgCNi3 and CdCNi3 Under Different Pressure

The second-order elastic constants (SOECs) and third-order elastic constants (TOECs) of MgCNi3 and CdCNi3 are presented by using first-principles methods combined with homogeneous deformation theory. The Voigt–Reuss–Hill (VRH) approximation are used to calculate the bulk modulus B, shear modulus G, averaged Young’s modulus E and Poisson’s ratio ν for polycrystals and these effective modulus are consistent with the experiments. The SOECs under different pressure of MgCNi3 and CdCNi3 are also obtained based on the TOECs. Furthermore, the Zener anisotropy factor, Chung–Buessem anisotropy index, and the universal anisotropy index are used to describe the anisotropy of MgCNi3 and CdCNi3. The anisotropy of Young’s modulus of single-crystal under different pressure is also presented.

Ab-initio investigations on elastic properties in L12 structure Al3Sc and Al3Y under high pressure

Abstract The effects of high pressure on elastic properties and electronic structures of L12 structure trialuminide Al3Sc and Al3Y compounds have been investigated by first-principles calculations within the local density approximation. The elastic properties and Debye temperature for Al3Sc and Al3Y increase with the increasing pressure, and the calculated values in elastic properties and Debye temperatures which obtained at 0 GPa are in good agreement with the available experiment data. The mechanical anisotropic properties are discussed using universal anisotropic index AU and Zener anisotropy index AZ. The calculated electronic properties suggest that a significant amount of charge in the interstitial region gives rise to an enhanced directional covalent-type bonding between the Sc (Y) and Al atoms as the pressure is up to 40 GPa.

Mechanical and thermodynamic properties of Al3Sc and Al3Li precipitates in Al–Li–Sc alloys from first-principles calculations

The mechanical, electronic and thermodynamic properties of L12-type Al3Sc and Al3Li precipitates have been investigated from first-principles method. The calculated equilibrium parameters such as lattice constants are in good agreement with the available experimental results and other theoretical reports. It is found that the Al3Sc exhibits a higher structural stability and stronger alloying ability than that of Al3Li since the Al3Sc possesses the lower cohesive energy and formation enthalpy. Mechanical parameters, such as the bulk modulus B, shear modulus G, Young's modulus E, Poisson's ratio ν and universal anisotropic index AU are determined by the Voigt–Reuss–Hill approximation. In addition, the anisotropic sound velocity, Debye temperature, density of states and charge density distribution of the two precipitates are studied. The calculations associated with phonon properties confirm the dynamical stability of the L12-type structures studied. Finally, the temperature-dependent behaviors of thermodynamic properties of the two precipitates are determined within the quasi-harmonic approximation.

Mechanical and electronic properties of Ag3Sn intermetallic compound in lead free solders using ab initio atomistic calculation

Abstract First principle calculations based on density functional theory (DFT) are used to calculate the structural, elastic and electronic properties of tin–silver intermetallic compound (Ag3Sn), found mainly in lead free solder joints. In present work, for the exchange-correlation energy, generalized gradient approximation (GGA) functional is used. The calculated lattice constants are found to be within 2% error of the experimental values. All single crystal elastic constants are computed from which values of shear modulus, bulk modulus, Young's modulus and Poisson's ratio for polycrystalline Ag3Sn are calculated using Voigt and Hill approximations. To explain the scatter in the experimentally determined values of elastic constants, directional dependence of bulk modulus and Young's modulus are estimated. The values of Young's modulus calculated along different planes are found to be in same range as experimentally determined values. Various anisotropic indices like universal anisotropic index, Zener anisotropic index, shear anisotropic index and others are calculated to study elastic anisotropy. Further anisotropy in Poisson's ratio is studied by calculating their values along six lower-index planes. The value of Debye temperature calculated using elastic data of present work is found be to higher than the values obtained using resistivity measurement, which can be attributed to temperature dependence. Electronic properties are studied via the band structure and total and partial density of states. The density of state (DOS) of Ag3Sn has a characteristic main peak which is mainly dominated by Ag-d states. At the Fermi level, the total DOS value is found to be 1.97 states/eV with major contribution coming from Sn p states and minor contribution from Sn s and Ag s, p and d states.

Elastic properties of YAG: First-principles calculation and experimental investigation

The hardness and elastic stiffness of Y3Al5O12 (YAG) were investigated by first-principles calculations and experiments. The mechanical properties including the second-order elastic coefficients, hardness, bulk modulus, Young's modulus and shear modulus were calculated by density functional theory (DFT). The calculated results were in good agreement with the experimental values. The hardness of YAG is mainly attributed to Altet–O bonds. The elastic anisotropy of YAG was discussed. Zener anisotropy parameter of YAG is close to unit and its universal anisotropy index is very close to zero, which indicates the structure of YAG is nearly centrosymmetric. The longitudinal and transverse sound velocities and Debye temperature were also investigated.